to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief-propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution. Our codes are found by optimizing the degree structure

show how explicitly incorporating the notion of 'sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data

consistent equations for the coding rules X → ˜ X and ˜ X → Y. Solutions to these equations can be found by a convergent re–estimation method that generalizes the Blahut–Arimoto algorithm. Our variational principle provides a surprisingly rich framework for discussing a variety of problems in signal

of the developers’ own hand-written test suite. When we did the same for 75 equivalent tools in the BUSYBOX embedded system suite, results were even better, including 100 % coverage on 31 of them. We also used KLEE as a bug finding tool, applying it to 452 applications (over 430K total lines of code), where

It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm

Abstract-It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit

, and thus it works at a lower level than abstract-syntax trees. But CIL is also more high-level than typical intermediate languages (e.g., three-address code) designed for compilation. As a result, what we have is a representation that makes it easy to analyze and manipulate C programs, and emit them in a

Software vulnerabilities have had a devastating effect on the Internet. Worms such as CodeRed and Slammer can compromise hundreds of thousands of hosts within hours or even minutes, and cause millions of dollars of damage [32, 51]. To successfully combat these fast automatic Internet attacks, we

Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon

that applies priority search on hierarchical k-means trees, which we have found to provide the best known performance on many datasets. After testing a range of alternatives, we have found that multiple randomized k-d trees provide the best performance for other datasets. We are releasing public domain code